This book presents applied probability and stochastic process in an elementary but mathematically precise manner, with numerous examples and exercises to illustrate the range of engineering and science applications for the concepts. The book is designed to give the reader an intuitive understanding of probabilistic reasoning, in addition to an understanding of mathematical concepts and principles. The initial chapters present a summary of probability and statistics and then Poisson processes, Markov chains, Markov processes and queueing processes are introduced. Advanced topics include simulation, inventory theory, replacement theory, Markov decision theory, and the use of matrix geometric procedures in the analysis of queues. Included in the second edition are appendices at the end of several chapters giving suggestions for the use of Excel in solving the problems of the chapter. Students will have access to the answers of odd numbered problems and instructors will be provided with a full solutions manual and Excel files when needed for homework. New in this addition are an introductory chapter on statistics that includes a section on risk assessment and a chapter on Poisson Processes. The old chapter on queues has been expanded and broken into two new one: one for simple queueing processes and one for queueing networks.